Intermediate Financial Theory, 3rd Edition

for any increasing, concave utility function U( ), where these expectations are “linear in the probabilities” as per VNM-expected utility theory.

If we further assume U( ) is homogeneous of degree ν and that the start-of-period wealth is Y₀, then

$\begin{array}{l}{Y}_0^{\nu }EU(1+{\tilde{r}}_{P*})>Y_0^{\nu }EU(1+{\tilde{r}}_P)\hfill \\ EU(Y_0(1+{\tilde{r}}_{P*}))>EU(Y_0(1+{\tilde{r}}_P))\hfill \end{array}$ (6.9)

(6.9)

for any increasing, concave utility function U( ). If our investor’s utility function is increasing, concave, and homogeneous, his expected utility will thus increase with the inclusion of A.

Note that expectations in Eq. (6.9) are ...